To begin, the correct term is "crossed" polarizer, not cross.
The way that a crossed polarizer works is that it contains two
polarizers, the first selects a plane of polarized light from an
unpolarized light source (containing many oscillations, or planes).
The second polarizer than absorbs that plane of polarized light
that made it past the first, as it selects a plane of polarized
light that is not the one let through the first.